Saturday, February 15, 2014

NBA Playoff Seed Probabilities - In Motion

This post is an updated version of a feature I published last year on NBA playoff seed probabilities. My daily ranking table features a bar graph for each team, summarizing their playoff (and lottery) seeding probabilities, where the probabilities come from a Monte Carlo simulation.

Improbably, I had the foresight to archive each day's playoff projections, which I can now turn into a dynamic motion chart. The bar graph below shows how each team's playoff chances have evolved on a daily basis, from early November all the way to the All Star break.

By mid-December, the Pacers had already locked up a one or two seed, while the Bucks were already out of playoff contention. The Trailblazers began the season as a likely #9 seed, but are now a lock for the playoffs and a good bet for a #2 or #3 seed.

Tuesday, February 4, 2014

The $1 Billion Bracket - Part Two

Bra-ket notation
This is part two of a two part post on the probability of a perfect bracket, motivated by Quicken Loans announcement that they will pay one billion dollars to anybody that can submit said perfect bracket. Part one used information from the betting markets, the moneyline to be exact, to get an order of magnitude estimate on the probability. For part two I will calculate the probability more directly, finding that the odds of picking a perfect bracket are about 1 in 50 billion when you have a reliable ranking methodology.

That high level analysis from part one resulted in a probability range of one in 500 trillion to 1 in 20,000 trillion. As I pointed out in part 1, this is much higher than the naive "50/50" estimate of 9.2 million trillions, but still well below estimates from math professor Jeff Bergen and "Numbers Guy" Carl Bialick.

The main drawback of my previous analysis is that it estimated the probability of a particular bracket, not an optimal one. In order to calculate the probability of an optimal bracket getting every game right, you need a way to rank every team in the NCAA and calculate the odds of winning for a matchup between any two teams.

Saturday, February 1, 2014

New Stat: "Kitchen Sink" Win Probability Added

I have added a new column to my player win probability page. For lack of a better term, I am calling it Kitchen Sink WPA (as in "everything but"). It quantifies the win probability contributions for every box score stat we can measure and attribute at the player level. That means it includes all the stats in my "official" WPA stat: shots (made and missed), getting to the foul line, free throws (made and missed), and turnovers. In addition, it includes Win Probability Added due to rebounds, assists, blocks, and steals.

This new stat will not replace my official definition of Win Probability Added, it's just an alternate way of looking at how a player has contributed to team wins. I consider this an unofficial stat because I think I'm adding apples and oranges here (or orange juice and toothpaste). Official WPA captures both the upside and downside of a particular subset of player contributions. It measures what a player does when entrusted with his team's possession.  WPA due to rebounds, assists, blocks, and steals are "plus only" stats. They can only help a player, which is why I have chosen not to include them in official WPA.

Here is the player win probability table sorted by "kitchen sink" WPA.

I have abbreviated the stat as "kWPA" in the table. As of February 1, Stephen Curry leads the league in kWPA. He was already number 13 in official WPA, and his 11.97 in assist WPA vaults him to the top of the rankings. In general, kWPA will be much kinder to point guards than official WPA. WPA, perhaps unfairly, counts turnovers but not assists. Point guards tend to have more turnovers not because they are bad ball handlers, but because they are usually tasked with running the offense and distributing the ball to their teammates.

Lebron James, a fixture at the top of the WPA rankings, also does well by the kWPA metric (#2, behind Curry). His chief competitor for WPA, Kevin Durant, is worse off, as he does not amass the kind of box score stats (particularly assists and rebounds) that Lebron does.